At the close of New York trade the Dow Jones Industrial Average was up 160.52 points (1.23 percent) at 13,241.25.
The broad-market S&P 500 gained 19.40 points (1.39 percent) to 1,416.51, while the tech-rich Nasdaq Composite added 54.65 (1.78 percent) to 3122.57.
Analysts credited the strong performance to rises in European markets and Bernanke's speech signaling he is still not too worried about inflation.
He "seemed to suggest that the Fed recognizes the need to remain accommodative in its policies, given that job market conditions remain far from normal," said Briefing.com.
"We cannot yet be sure that the recent pace of improvement in the labor market will be sustained," Bernanke said in a speech outside Washington.
"Further significant improvements in the unemployment rate will likely require a more-rapid expansion of production and demand from consumers and businesses, a process that can be supported by continued accommodative policies."